MS Access to MySQL - Database Conversion

Hello everyone I have a site which uses a Microsoft Access database, connected through ODBC. This is currently hosted on a Windows NT Machine, without problems. Now it needs to be ported to a Linux machine - and a MySQL database. My Question: What is the easiest way to convert the data from one database to the next? Secondly - I haven't dealt with MySQL before - how much of the code will need to be changed for it to work with the MySQL database? If there's too much work involved, I may stick with the Access database. How can this be setup on the linux machine? It it was possible - would the code need to be changed? Thanks everyone - I look forward to your reply's. Tom Peck